Newton's Results for the orbits of the planets

Using his three laws and the law of gravity Newton predicted ...
(well, first he had to invent calculus) What Newton derived was Kepler's three laws. The laws were already known, of course, but it wasn't known where they came from. Newton showed that the same laws of mechanics that govern the motion of objects on earth also govern the motion of the planets.

We can use this relation to find the mass of a planet if it has a moon (or a space probe) orbiting it. If we know P and a we can use

To get the sum of the masses of the planet ( m1) and the mass of the moon (m2). Typically, the mass of the moon is negligably small compared to the mass of the moon. Then we have

Study hint: These last three formulas are a little complicated. For our purposes, it is enough to remember Kepler's Third Law, that P2 = constant * a3 for all of the planets in the solar system or (with a different constant) for all of the moons orbiting Jupiter. Then we need to understand that from the motions of Jupiter's moons we can find the mass of Jupiter, but I do not recommend memorizing these three formulas.

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Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA